POLARIMETRY

477

from

shadow angle. Further, as will be seen later, it is not desirable to make this half-shadow angle too great, as the sensitiveness is reduced proportionately.

§ (5) THE LAURENT POLARIMETEU. — In order to overcome this defect in the Cornu-Jellett polariser, Laurent 1 used a quartz plate covering half of a plane polarised beam from a Nicol prism. The principle can be understood The quartz plate A, whose optic axis lies in the plane of the paper, and has a direction OB, covers half of the circular aperture of the field of the Nicol prism in front of it. The thickness of the plate is chosen so that the difference between the paths of the ordinary and extraordinary rays, into which the incident plane polarised beam is divided, is some odd multiple of half the wave-length of the light that is used. If n0 and ne are the refractive indices of the ordinary and extraordinary rays in the quartz for a given wave-length X, then

5=d(ne -n0)= (2m +1 )g,

when d is the thickness of the plate, and S the path difference introduced. For 'the sodium light T)t and D2 the minimum thickness is 0-0324 mm., but, as this plate would be too thin and fragile in practical use, some odd multiple of this thickness is chosen so that the plate is approximately -5 mm. thick.

Let OE represent the plane of polarisation, and its length the amplitude of the linearly polarised homogeneous light coming from the polariser, whose plane of polarisation makes an angle 0/2 with the optic axis OB of the quartz plate. The plane polarised beam, the direction and amplitude of which is given by OE, will, on entering the quartz plate, be divided into two parts, the one polarised in the plane of the optic axis OB and the other perpendicular to it in the plane CD. Thus OGr and OK will represent the amplitudes and directions of the components at the moment that OE enters the plate. These components are in phase with each other.

Since the component of the beam represented by OK is accelerated in its passage through the quartz by an amount (2m+l)X/2, m being an integer, as compared with the extraordinary ray OG, the position at emergence can be represented graphically by reversing the direction of OK, the components in phase on emergence being OG and OJ. Thus the

1 Laurent. Journ. d. Phus., 1874 (T.). ill. 183; 1870, viii. 104; Dingler's Poly. Journ., 1877, ccxxiii. 608.

resultant OF will represent the plane of polarisation after transmission of the beam through the quartz. If CD represents the plane of polarisation of the analyser, then a matching of the fields is obtained when the component OJ on CD is equal to the component OK from the unobstructed half of the field.

In order to vary the half-shadow angle, all that is required is to rotate .the plane of polarisation of the polarising nicol; the angle that this plane makes with the optic axis of the plate is one-half the half-shadow angle.

This Laurent polariser, while allowing a variable half-shadow angle, is limited as to light source, the only permissible one being that for which the half-wave plate has been cut. / The sensitiveness, as in all half-ahadow polarisers, depends upon the magnitude of this angle, and on the intensity of the light source used. Heele 2 somewhat increased the sensitiveness by arranging the half-wave plate as a circular one mounted on a larger glass plate, as in Fig. 9 (i.), and Pellin has introduced the modification shown in Fig. 9 (ii.), when the retarding plate forms a ring around the centre of the field as shown.

When using a bright sodium light with a small half-shadow angle (about the precaution suggested by Laurent of using a thin plate of potassium bichromate to cut off the other radiations of sodium, consistent settings can be made to within + J'.

Lippich8 has, however, shown that the Laurent polariser cannot bo relied on as an exact means of measurement. Since the relative importance of this type of polariser has become considerably smaller during the last twenty years, it will bo sufficient to mention some of the main results of Lippich's analysis'. The technical difficulties of making the plates perfectly parallel, with the optic axis lying exactly in the same plane, and of exactly the correct thickness for the particular wave-length chosen, are with modern methods perhaps not insuperable. But Lippioh found that they certainly were not made with sufficient accuracy; and even had they been ideally perfect it would have been necessary, in order that different instruments might agree, that the thicknesses of all Laurent plates should be identical, and not merely any odd number of half-wave-length retardation. Again, even if agreement were thus secured, the precise significance of rotation measurements depended on a knowledge of the rotatory dispersion of the substance under test, which knowledge could not be obtained on instruments of the Laurent type.

Finally, one and the same instruments give different measurements of a rotation with different half-

2 Heele, Zeitsch. Instkde., 1896, xvi. 269. 8 Lippich, Site. Wien. AkatL., 1890, abt. Ila, xcix. 695.

and taking